Indeed!
Goedel and Turing proved that it could not be done, that there was no way to
formalise mathematics into crystal clear Black And White.
Hilbert proposed that there should be a set of rules so that everyone could
agree on a proof..that it is either correct or incorrect.
An artificial language should have been developed is what he thought, and
then from that you could get Absolute Truth.
Mathematicians thought that Absolute Truth was theirs and theirs alone. This
is where Math confuses me..it is as much a philosophy as a 'science'.
Anyways, G�del shocked the world by showing them that this Absolute Truth
thing was impossible, and just couldn't work.G�del did this in 1931, and
afterward Turing went more into it, but in a nutshell here's what G�del did
to prove that poor Hilebert and all the others espousing his views were
wrong.
G�del started off by saying: This Statement Is False.
What I am saying is a lie, I am lying..
But If I am Lying..and it is a Lie that I am lying..then I am telling the
Truth!
So saying This Statement Is False, is false if and only if it is True.
So G�del then stated that This Statement Is Unprovable..
(within the confines of Hilbert's axiomatic system which he was trying to
create.)
Turing then took this a bit further, and arguably it was HE that first
invented the computer..on paper in 1936.
now of course Turing didn't know what a computer was, so he had to come up
for a word to describe it..so he came up with the Turing Machine. But in
essence what he described were general purpose computers!
It was through the use of this theory, on paper, that Turing discovered the
Halting Problem, that further trashed Hilbert's dream of an Absolute Truth
Utopia.
The Halting problem says that there is no way to tell if a computer program
will EVENTUALLY Halt!
Yes..if you think about it for a while it is true.
You could conceivably write a coldfusion script that would supposedly cycle
through a table which it self populates with data based on previous
values..and hey it should keep running for ever..but you don't KNOW
that..because you CAN'T keep it running forever.
The only way for you to solve this problem, is by putting a time limit on
how long the program runs. Either by setting Disk Space size, or number of
iterations.
But if you don't put a limit on it, then you can't really tell if it will
halt or not..and this is the important point that Turing was trying to make.
The point is to realise that you have to give up. You can't do it.
So there is no mechanical, or logical procedure that can determine if a
program will halt or not... and therefore it turns out that there is no SET
of mathematical axioms as described by Hilbert, that will determine whether
a program will halt or not.
Therefore the statement made by Metamath is provably FALSE!
And that's the Absolute Truth!
:-)
Hence...Math on the whole, Theoretical math especially..is all Bull sh**!
Come again Dances With Horsies!
-Gel
zwibble dee bubble..
wubbles dee woo..
Fly Away Fly Away
We All Fall Down!
e0
x = wx
-----Original Message-----
From: Michael Smith [mailto:[EMAIL PROTECTED]]
Sent: Tuesday, April 24, 2001 5:37 PM
To: CF-Community
Subject: Re: Remember All That Talk About Math?
I thought Godel's Theorem proved that this was impossible. That any system
that was built from set theory that
included simple arithmetic must be self contradictory....
- Michael Smith, TeraTech, Inc http://www.teratech.com/
Erika L Walker wrote:
> I found this to be rather fascinating...
>
> "Essentially everything that is possible to know in mathematics can be
> derived from a handful of axioms known as "Zermelo-Fraenkel set theory,"
> which is the culmination of many years of effort to isolate the essential
> nature of mathematics and is one of the most impressive achievements of
> humankind. The Metamath Proof Explorer will let you drill down any of its
> proofs directly to these axioms.
>
> While it might be helpful to have some logic background for a high-level
> understanding, in principle you need no prior knowledge to mechanically
> follow any proof."
>
> http://metamath.planetmirror.com/
>
> Erika
>
> "You have to laugh at yourself because you'd cry your eyes out if you
> didn't." - Emily Saliers
>
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